Faults in Earth's crust accommodate slow relative motion between tectonic plates through either similarly slow slip or fast, seismic-wave-producing rupture events perceived as earthquakes(1-3). These types of behaviour are often assumed to be separated in space and to occur on two different types of fault segment: one with stable, rate-strengthening friction and the other with rate-weakening friction that leads to stick-slip(2-5). The 2011 Tohoku-Oki earthquake with moment magnitude M-w = 9.0 challenged such assumptions by accumulating its largest seismic slip in the area that had been assumed to be creeping(6-10). Here we propose a model in which stable, rate-strengthening behaviour at low slip rates(11,12) is combined with coseismic weakening due to rapid shear heating of pore fluids(13-16), allowing unstable slip to occur in segments that can creep between events. The model parameters are based on laboratory measurements on samples from the fault of the M-w 7.6 1999 Chi-Chi earthquake(17). The long-term slip behaviour of the model, which we examine using a unique numerical approach that includes all wave effects(16,18), reproduces and explains a number of both long-term and coseismic observations-some of them seemingly contradictory-about the faults at which the Tohoku-Oki and Chi-Chi earthquakes occurred, including there being more high-frequency radiation from areas of lower slip(8,19-21), the largest seismic slip in the Tohoku-Oki earthquake having occurred in a potentially creeping segment(6,7), the overall pattern of previous events in the area(8) and the complexity of the Tohoku-Oki rupture(9). The implication that earthquake rupture may break through large portions of creeping segments, which are at present considered to be barriers, requires a re-evaluation of seismic hazard in many areas.